FPSAC 2024 Ruhr-Universität Bochum

Conference Schedule

On this Page

  1. Week Overview
  2. Daily View
  3. Titles and Abstracts of Invited Speakers
  4. Tribute to Ian Macdonald

Week Overview

All Lectures take place in the main lecture hall of the IC building (HIC).

Daily View

Sunday

Time Speaker Notes
17:00 – 20:00 Welcome Reception at the mensa ( = dining hall)

Monday

Lectures take place in the main lecture hall of the IC building (HIC).

Session Chairs

Time Speaker Notes
8:00 – 8:45 Registration in HIC
8:45 – 9:00 Opening Remarks in HIC
9:00 – 10:00 Josephine Yu
Real Tropical Geometry, Determinants, and Matroidal Structures
Abstract
10:00 – 10:30 Changxin Ding
A framework unifying some bijections for graphs and its connection to Lawrence polytopes
Extended Abstract
10:30 – 11:00 Coffee Break in ID 04/459 and ID 04/471
11:00 – 11:30 Leo Jiang
Real matroid Schubert varieties, zonotopes, and virtual Weyl groups
Extended Abstract
11:30 – 12:00 Jeanne Scott
Diagram model for the Okada algebra and monoid
Extended Abstract
12:00 –14:00 Lunch  
14:00 – 15:00 Carolina Benedetti
On flags of positroids: enumerative and geometric aspects via lattice path matroids
Abstract
15:00 – 15:30 Steven Karp
Universal Pluecker coordinates for the Wronski map and positivity in real Schubert calculus
Extended Abstract
15:30 – 16:00 Coffee Break in ID 04/459 and ID 04/471
16:00 – 16:30 Patricia Commins
Invariant theory for the face algebra of the braid arrangement
Extended Abstract
16:30 – 17:00 Gaku Liu
A regular unimodular triangulation of the matroid base polytope
Extended Abstract
17:00 – 18:00 Arun Ram
Ian G. Macdonald: Works of Art
Abstract

Tuesday

Lectures take place in the main lecture hall of the IC building (HIC).

Session Chairs

Time Speaker Notes
9:00 – 10:00 Rosa Orellana
See-Saw Pairs and Plethysm
Abstract
10:00 – 10:30 Damián de la Fuente
On the size of Bruhat intervals
Extended Abstract
10:30 – 11:00 Coffee Break in ID 04/459 and ID 04/471
11:00 – 11:30 Tianyi Yu
Analogues of two classical pipedream results on bumpless pipedreams
Extended Abstract
11:30 – 12:00 Christian Gaetz
Pattern heights and the minimal power of \(q\) in a Kazhdan–Lusztig polynomial
Extended Abstract
12:00 –12:30 Conference Photo  
12:30 –14:00 Lunch  
14:00 – 15:00 Satoshi Murai
Stanley-Reisner rings and triangulated manifolds
Abstract
15:00 – 15:30 Eva Philippe
Realizing the \(s\)-permutahedron via flow polytopes
Extended Abstract
15:30 – 16:00 Coffee Break in ID 04/459 and ID 04/471
16:00 – 16:30 Matias von Bell
Framing lattices and flow polytopes
Extended Abstract
16:30 – 17:00 Vincent Pilaud
Acyclonestohedra
Extended Abstract
17:00 – 18:30 Poster Session 1 in the coffee break area

Wednesday

Lectures take place in the main lecture hall of the IC building (HIC).

Session Chair

Cynthia Vinzant

Time Speaker Notes
9:00 – 10:00 Kris Shaw
Patchworking in higher codimension and oriented matroids
Abstract
10:00 – 10:30 Philippe Nadeau
Smirnov words and the Delta conjectures
Extended Abstract
10:30 – 11:00 Coffee Break in ID 04/459 and ID 04/471
11:00 – 11:30 Wenjie Fang
Tamari intervals and blossoming trees
Extended Abstract
11:30 – 12:00 Greta Panova
All Kronecker coefficients are reduced Kronecker coefficient
Extended Abstract
12:00 – 13:00 Lunch  
13:00 – 20:00 Excursions  

Thursday

Lectures take place in the main lecture hall of the IC building (HIC).

Session Chairs

Time Speaker Notes
9:00 – 10:00 Markus Reineke
Motivic generating series of quiver representations
Abstract
10:00 – 10:30 Matteo Parisi
Cluster algebras and tilings for the \(m=4\) amplituhedron
Extended Abstract
10:30 – 11:00 Coffee Break in ID 04/459 and ID 04/471
11:00 – 11:30 Florian Schreier-Aigner
\(qtRSK^∗\): A probabilistic dual RSK correspondence for Macdonald polynomials
Extended Abstract
11:30 – 12:00 Ricky Liu
Plane partitions and rowmotion on rectangular and trapezoidal posets
Extended Abstract
12:00 – 12:30 FPSAC 2025 Announcement  
12:30 – 14:00 Lunch  
14:00 – 15:00 Lisa Sauermann
The Erdős–Ginzburg–Ziv Problem in Discrete Geometry
Abstract
15:00 – 15:30 Zhongyang Li
Asymptotics of Bounded Lecture-Hall Tableaux
Extended Abstract
15:30 – 16:00 Coffee Break in ID 04/459 and ID 04/471
16:00 – 16:30 Pierre Bonnet
A Galois structure on the orbit of walks in the quadrant
Extended Abstract
16:30 – 17:00 Valentin Feray
A determinantal point process approach to scaling and local limits of random Young tableaux
Extended Abstract
17:00 – 18:30 Poster Session 2 in the coffee break area
19:00+ Banquet at at the mensa ( = dining hall)

Friday

Lectures take place in the main lecture hall of the IC building (HIC).

Session Chairs

Time Speaker Notes
9:00 – 10:00 Nicholas Proudfoot
Categorical valuations for polytopes and matroids
Abstract
10:00 – 10:30 Nicolle Gonzalez
Triangular \((q, t)\)-Schroder Polynomials and Khovanov-Rozansky Homology
Extended Abstract
10:30 – 11:00 Coffee Break in ID 04/459 and ID 04/471
11:00 – 11:30 Christin Bibby
Supersolvable posets and fiber-type arrangements
Extended Abstract
11:30 – 12:00 Shuhei Tsujie
The characteristic quasi-polynomials for exceptional well-generated complex reflection groups
Extended Abstract
12:00 – 14:00 Lunch  
14:00 – 15:00 Michael Joswig
Hypersimplices, tropical geometry and finite metric spaces
Abstract
15:00 – 15:30 Anastasia Nathanson
Chow rings of matroids as permutation representations
Extended Abstract
15:30 – 16:00 Coffee Break in ID 04/459 and ID 04/471
16:00 – 16:30 Jonah Berggren
Wilting Theory of Flow Polytopes
Extended Abstract
16:30 – 17:00 Nathan Williams
Charmed roots and the Kroweras complement
Extended Abstract
17:00 – 17:30 Closing Remarks  
17:30 – 19:00 Ice Cream Social  


Titles and Abstracts of Invited Speakers

Carolina Benedetti

Title: On flags of positroids: enumerative and geometric aspects via lattice path matroids

Abstract: Positroids are a family of representable matroids that have gain lots of attention in enumerative and algebraic combinatorics, in tropical geometry and in physics. Lattice path matroids (LPMs) are a subclass of positroids that are very well behaved. In particular, LPMs provide (regular) subdivisons of the uniform matroid \(U_{k,n}\). Subdivisions of \(U_{k,n}\) into positroids have been studied in the last years by various authors, in the context of nonnegativity in tropical geometry. On the other hand, the permutahedron \(P_n\) can be thought as the flag matroid whose constituents are \(U_{1,n}, U_{2,n},...,U_{n,n}\). Subdivisions of \(P_n\) into flags of positroids appear in recent work of several authors, in the context of the nonnegative tropical flag variety. In this talk we will explore flags of positroids focusing on flags of LPMs, as well as subdivisions of \(P_n\) into LPMs and will interpret these results in various contexts. This is current work with K. Knauer.

Michael Joswig

Title: Hypersimplices, tropical geometry and finite metric spaces

Abstract: The hypersimplex \(\Delta(k,n)\) is the convex polytope which is the set of those points in the unit cube \([0,1]^n\) which satisfy the affine linear equation \(\sum x_i=k\). We report on known and new results concerning the secondary fan \(\Sigma(k, n)\), which stratifies the regular subdivisions of \(\Delta(k,n)\). For tropical geometry this is relevant because \(\Sigma(k,n)\) contains the tropical Grassmannian \({\rm TGr}(k,n)\) as a subset; we discuss that relationship. Furthermore, in the special case \(k = 2\) the fan \(\Sigma(2,n)\) is closely related to the metric fan \({\rm MF}(n)\), which forms a natural parameter space for the metric spaces on \(n\) points. Our analysis of the fans \(\Sigma(2,n)\) improves known results of Bandelt and Dress concerning structural properties of finite metric spaces, with applications to phylogenetics. The new results are joint work with Laura Casabella and Lars Kastner.

Satoshi Murai

Title: Stanley-Reisner rings and triangulated manifolds

Abstract: Applications of Stanley-Reisner rings to combinatorics of simplicial complexes is classical in algebraic combinatorics. In particular, this approach has yield various important combinatorial results on simplicial polytopes and triangulated spheres since their Stanley-Reisner rings have nice algebraic properties. In the last 15 years, it has been found that classical results on Stanley–Reisner rings of polytopes and spheres can be naturally generalized to triangulated manifolds, and these generalizations have been applied to study combinatorial properties of triangulated manifolds. In this talk, I will show key algebraic results on this topic and explain how these algebraic results are applied to study combinatorics of triangulated manifolds.

Rosa Orellana

Title: See-Saw Pairs and Plethysm

Abstract: The Plethysm problem asks for a combinatorial interpretation of the coefficients which occur in the composition of two polynomial representations of the general group. Making progress even for special cases has proven to be extremely difficult. The plethysm coefficients occur in many other problems in algebraic combinatorics such as the restriction problem, which asks for a combinatorial interpretation to the coefficient occurring when a polynomial representation of the general linear group is restricted to the symmetric group (realized as permutation matrices). Other problems related to plethysm are finding symmetric chain decompositions for the truncated Young lattice and Foulkes’ conjecture.

In this talk I will describe how the representation theory of diagram algebras gives another interpretation to the plethysm problem. The connection to diagram algebras is achieved using see-saw pairs and centralizer algebras which uses the representation theory of a subalgebra of uniform block permutations of the partition algebra. This leads to a new approach to an important special case of the plethysm problem which would lead to solutions to the restriction, symmetric chain decomposition problem, and Foulkes’ conjecture. This is joint work with F. Saliola, A. Schilling, and M. Zabrocki.

Nicholas Proudfoot

Title: Categorical valuations for polytopes and matroids

Abstract: A polytope valuation is an invariant that is additive under decompositions of polytopes into smaller polytopes. A matroid valuation is similar, with a focus on base polytopes of matroids. This property is extremely useful for calculations and also surprisingly common. I will describe a way to categorify the notion of a valuation, with two goals in mind. The first is to provide a more satisfying explanation for why certain invariants are valuations. The second is to perform richer calculations that take into account the actions of symmetry groups of polytopes or matroids.

Markus Reineke

Title: Motivic generating series of quiver representations

Abstract: We introduce generating series “counting” representations of quivers and discuss structural properties such as product factorizations and functional equations, and their relation to algebraic combinatorics and moduli spaces.

Lisa Sauermann

Title: The Erdős–Ginzburg–Ziv Problem in Discrete Geometry

Abstract: The Erdős–Ginzburg–Ziv Problem is a classical extremal problem in discrete geometry. For given positive integers \(m\) and \(n\), it asks the following question: What is the minimum number \(s\) such that among any \(s\) points in the \(n\)-dimensional integer lattice \(\mathbb{Z}^n\) there are always \(m\) points whose centroid is also a lattice point? It turns out that it essentially suffices to consider the case where \(m=p\) is a prime number, and that the problem then naturally translates into a problem over the finite field \(\mathbb{F}_p\). A wide range of different algebraic techniques can be used to approach this problem in different ranges for \(p\) and \(n\). This talk will give an overview of the known bounds for the problem, and of the different techniques that were used to obtain them. A particular focus of the talk will be the case where \(m=p\) is a fixed prime and \(n\) is large with respect to \(p\).

Kris Shaw

Title: Patchworking in higher codimension and oriented matroids

Abstract: The Ardila-Klivans fan of a matroid provides a direct link between matroids and toric/tropical geometry and has had impressive applications in recent years. In this talk, I will provide a cryptomorphic description of a matroid orientation, known as a real phase structure. Via a generalisation of Viro’s patchworking procedure this provides a link between oriented matroids and real toric varieties and even a homological obstruction to matroid orientation.

Real phase structures are also obtained when tropicalising a real algebraic variety. When the tropicalisation is locally matroidal, I will explain how the tropicalisation together with the real phase structure can be used to recover the topology of a real algebraic variety near the tropical limit. Finally, the topology of these real algebraic varieties, and more general patchworks, can be studied by adapting a spectral sequence from the case of hypersurfaces. This spectral sequence arises from filtrations of the tope space of an oriented matroid.

This talk is based in part on joint work with Allermann & Rau and Yuen.

Josephine Yu

Title: Real Tropical Geometry, Determinants, and Matroidal Structures

Abstract: I will discuss how tropical geometry reveals matroidal structures in certain real algebraic geometric objects. Brändén showed in 2010 that tropicalization of stable polynomials, including some determinantal polynomials arising from positive semidefinite matrices, exhibit M-convexity introduced by Murota (M stands for matroids). Brändén’s result was later extended to Lorentzian polynomials and positively hyperbolic varieties. I will provide an overview of tropicalization, survey these results, and present our new joint work with Abeer Al Ahmadieh, Felipe Rincón, and Cynthia Vinzant on studying the tropicalization of principal minors of positive semidefinite matrices using M-convexity, tropical Grassmannians, and tropical flag varieties.

Tribute to Ian Macdonald

Title: Ian G. Macdonald: Works of Art

Speaker: Arun Ram

Abstract: Ian Macdonald’s works changed our perspective on so many parts of algebraic combinatorics and formal power series. This talk will display some selected works of the art of Ian Macdonald, representative of different periods of his oeuvre, and analyze how they resonate, both for the past development of our subject and for its future.